Weighted Hypernetworks

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we extend the concept of evolving models of complex networks to hypernetworks. In this work, we firstly propose a non-uniform hypernetwork model with attractiveness, and obtain the stationary average hyperdegree distribution of the non-uniform hypernetwork. Furthermore, we develop a model for weighted hypernetworks that couples the establishment of new hyperedges and nodes and the weights' dynamical evolution. We obtain the stationary average hyperdegree and hyperstrength distribution by using the hyperdegree distribution of the hypernetwork model with attractiveness, respectively. In particular, the model yields a nontrivial time evolution of nodes' properties and scale-free behavior for the hyperdegree and hyperstrength distribution. It is expected that our work may give help to the study of the hypernetworks in real-world systems.